Integral equation solvers for real world applications - some challenge problems

Chew, Weng Cho; Chiang, I-Ting; Davis, C.P.; Hesford, Andrew J.; Li, M.K.; Liu, Yin; Qian, Zhiguo; Saville, Michael A.; Sun, Lin; Tong, Mei Song; Xiong, Jin; Jiang, Li Jun; Chao, Hsueh-Yung; Chu, Yunhui

doi:10.1109/aps.2006.1710460

Cited by 8 publications

(5 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Accurate solution of EM problems with conductive media requires to consider the loss or finite conductivity of the media in modeling and simulation, especially when the frequency is low or the conductivity is small since the skin depth is large [2]. While the problems can be solved with the robust finite element method (FEM) or other differential equation method (DEM) [3], we use the integral equation method (IEM) to solve them here because the IEM has a smaller solution domain, a better scaling property for computational costs, and no need of implementing an absorbing boundary condition (ABC) compared with the DEM [4] IEM, one usually relies on the surface integral equations (SIEs) with an approximate impedance boundary condition (IBC) [5]. The IBC has been widely studied [6]- [11] because it can dramatically simplify the solved problems, but it also requires that the skin depth be small for conductive media [12].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic Analysis for Conductive Media Based on Volume Integral Equations

Tong

Zhang

Wang

et al. 2014

IEEE Trans. Antennas Propagat.

View full text Add to dashboard Cite

Accurate electromagnetic (EM) analysis for conductive media requires to consider the finite conductivity of the media. Although the problems can be formulated by surface integral equations (SIEs) with an approximate surface impedance, we treat the conductive media as penetrable objects and use volume integral equations (VIEs) to exactly describe their EM features. The VIEs are solved by a point-matching scheme which does not rely on any basis and testing functions and allows the use of nonconforming meshes. Since the VIEs are well-conditioned in general and the integral kernels are free of material parameters, the scheme is flexible to accommodate a wide range of skin depth. Moreover, when the skin depth is small, we can only discretize the skin domain with a current distribution to reduce the cost. For large conductive media, we also incorporate the scheme with the multilevel fast multipole algorithm (MLFMA) to accelerate the solution. Typical numerical examples are presented to illustrate the scheme and its effectiveness has been validated.Index Terms-Conductive media, electromagnetic analysis, multilevel fast multipole algorithm, point-matching method, volume integral equations.

show abstract

Section: Introductionmentioning

confidence: 99%

Electromagnetic Analysis for Conductive Media Based on Volume Integral Equations

Tong

Zhang

Wang

et al. 2014

IEEE Trans. Antennas Propagat.

View full text Add to dashboard Cite

show abstract

“…The matrix decomposition algorithm–singular‐value decomposition (MDA–SVD) is another popular iterative solution used to analyze the scattering/radiation , which exploits the well‐known fact that for well‐separated subscatterers, the corresponding submatrices are of low rank and can be compressed. The system matrix resulting from EFIE is often an ill‐conditioned matrix and results in the low convergence of the Krylov iterative method . Although both the numerical complexity and the storage requirement of the iterative solution are less than that of the direct solution, the convergence rate of the iterative solution can vary in an unpredictable way.…”

Section: Introductionmentioning

confidence: 99%

The modified multilevel compressed block decomposition algorithms for analyzing the scattering of objects in half space

Ding

Shen

Jiang

et al. 2013

Int J Numerical Modelling

View full text Add to dashboard Cite

The convergence rate of iterative methods can vary in an unpredictable way. It is related to the matrix condition number, which is notoriously bad for the electric field integral equation in the large‐scale electromagnetic problems. Therefore, an efficient direct solution—a multilevel compressed block decomposition (MLCBD) algorithm based on the adaptive cross‐approximation algorithm—is applied to overcome this problem; it is very efficient for the monostatic problems. Simulation results of the objects up and below ground in half space demonstrate that the proposed MLCBD method is efficient for analyzing electromagnetic problems. Copyright © 2013 John Wiley & Sons, Ltd.

show abstract

“…The system matrix resulted from EFIE with the higher order hierarchical basis functions is often an ill-conditioned matrix and results in the low convergence of the Krylov iterative method [18]. Simple preconditioners like the diagonal or diagonal blocks of the coefficient matrix can be effective only when the matrix has some degree of diagonal dominance [19].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Sai Preconditioning Technique for Higher Order Hierarchical MLFMM Implementation

Ding¹,

Chen²,

Fan³

2008

PIER

View full text Add to dashboard Cite

Abstract-A new set of higher order hierarchical basis functions based on curvilinear triangular patch is proposed for expansion of the current in electrical field integral equations (EFIE) solved by method of moments (MoM). The multilevel fast multipole method (MLFMM) is used to accelerate matrix-vector product. An improved sparse approximate inverse (SAI) preconditioner in the higher order hierarchical MLFMM context is constructed based on the nearfield matrix of the EFIE. The quality of the SAI preconditioner can be greatly improved by use of information from higher order hierarchical MLFMM implementation. Numerical experiments with a few electromagnetic scattering problems for open structures are given to show the validity and efficiency of the proposed SAI preconditioner.

show abstract

Integral equation solvers for real world applications - some challenge problems

Cited by 8 publications

References 20 publications

Electromagnetic Analysis for Conductive Media Based on Volume Integral Equations

Electromagnetic Analysis for Conductive Media Based on Volume Integral Equations

The modified multilevel compressed block decomposition algorithms for analyzing the scattering of objects in half space

An Efficient Sai Preconditioning Technique for Higher Order Hierarchical MLFMM Implementation

Contact Info

Product

Resources

About